Median Absolute Deviation

What is the Median Absolute Deviation

The median absolute deviation(MAD) is a robust measure of how spread out a set of data is. The variance and standard deviation are also measures of spread, but they are more affected by extremely high or extremely low values and non normality. If your data is normal, the standard deviation is usually the best choice for assessing spread. However, if your data isn’t normal, the MAD is one statistic you can use instead.

The formula is a variation of the mean absolute deviation formula (see the mean absolute deviation article for more help in solving the formula). It is less affected by outliers because outliers have a smaller effect on the median than they do on the mean.

The term median absolute deviation refers to a statistic calculated from a sample. However, it can be used to estimate the population parameter.

MAD Example

Example: Find the MAD of the following set of numbers: 3, 8, 8, 8, 8, 9, 9, 9, 9.Step 1: Find the median. The median for this set of numbers is 8.